The laplacian on riemannian manifolds is an essential linear operator , and it is also the main object to be studied of geometric analysis on manifolds Riemann流形上的laplace算子是一个重要的线性算子，也是流形上几何分析研究的主要对象之一。
Linear preserver problem ( lpp for short ) concerns the characterization of linear operators on matrix spaces that leave certain functions , subsets , relations , etc . , invariant 线性保持问题（简称lpp ）刻画在矩阵空间上保持特定的函数，子集，关系等不变的线性算子
In order to characterize the linear operators that strongly preserve nilpotence and that strongly preserve invertibility , we first study the case of the binary boolean algebra 为了刻画强保持幂零的线性算子和强保持可逆的线性算子，我们首先研究二元布尔代数上的情况
In this paper , we characterize the linear operators preserving adjoint matrices on the spaces of all matrices , symmetric matrices and upper triangular matrices over domain 摘要木文刻画了整环上的全矩阵空间、对称矩阵空间和上三角矩阵空间上保持伴随矩阵的线性算子的结构。
By the means of the extension of linear operator , we characterize the linear operators that strongly preserve nilpotence and that strongly preserve invertibility over any boolean algebra 再利用线性扩张这一工具,我们刻画了在一般布尔代数上强保持幂零的线性算子和强保持可逆的线性算子
In this paper , we shall characterize the linear operators that strongly preserve nilpotent matrices and that strongly preserve invertible matrices over boolean algebras and antinegative semirings without zero divisors 本文将刻画在布尔代数和非负无零因子半环上强保持幂零矩阵和可逆矩阵的线性算子
In this thesis , based on principal component analysis ( pca ) , covariance stationary processes and spectral analysis theory of linear operator , spectral principal component analysis ( spca ) is put forward 在主成分分析的基础上，基于协方差平稳过程理论和线性算子谱分析理论，本文提出了谱主成分分析。
The paper will apply the methods of differential dynamical system and of functional analysis to the study of a series of linear operators and semigroup - nonwandering semigroup in chaotic dynamical system 本文将利用微分动力系统和泛函分析的方法，着重研究混沌动力学中的一类线性算子以及算子半群? ?非游荡算子半群。
The study of direct and inverse theorems on the approximation of linear operators to functions in normed linear spaces is an important subject in the approximation theory . it is significant in theory and application 线性算子对赋范线性空间中函数逼近正逆定理的研究是逼近论中重要的研究课题之一，在理论和实际应用上都具有重要的意义。
Also , by the means of the pattern of matrix and the pattern of linear operator , we characterize the linear operators that strongly preserve nilpotence and that strongly preserve invertibility over antinegative commutative semirings without zero divisors 另外,利用矩阵模式和算子模式等工具，我们在非负无零因子半环上刻画了强保持幂零的线性算子和强保持可逆的线性算子
